r"""
Python module for OEIS sequence number A064389.

Variation (4) on Recaman's sequence (A005132): to get a(n), we first
try to subtract n from a(n-1): a(n) = a(n-1) - n if positive and not
already in the sequence; if not then we try to add n: a(n) = a(n-1) + n
if not already in the sequence; if this fails we try to subtract
n+1 from a(n-1), or to add n+1 to a(n-1), or to subtract n+2, or to
add n+2, etc., until one of these produces a positive number not
already in the sequence - this is a(n).

Examples of use.
-----------------------------------------------------------------------
>>> from a064389 import *
>>> print a064389_list(15)
[1, 3, 6, 2, 7, 13, 20, 12, 21, 11, 22, 10, 23, 9, 24]
>>> print a064389_offset
1
>>> for x in a064389_list_pairs(6):
...     print x
...
(1, 1)
(2, 3)
(3, 6)
(4, 2)
(5, 7)
(6, 13)
>>> print a064389(7)
20
-----------------------------------------------------------------------
"""

from itertools import islice, izip, count

__all__ = ('a064389_offset', 'a064389_list', 'a064389_list_pairs', 'a064389', 'a064389_gen')
__author__ = 'Nick Hobson <nickh@qbyte.org>'

a064389_offset = offset = 1

def a064389_gen():
    """Generator function for OEIS sequence A064389."""
    s, x = set(), 0
    for n in count(1):
        y = x
        m = -n
        x = y + m
        while not (x > 0 and x not in s):
            m = -m if m < 0 else -(m + 1)
            x = y + m
        s.add(x)
        yield x

def a064389_list(n):
    """Returns a list of the first n >= 0 terms."""
    if n < 0: raise ValueError, 'Input must be a non-negative integer'
    return list(islice(a064389_gen(), n))

def a064389_list_pairs(n):
    """Returns a list of tuples (n, a(n)) of the first n >= 0 terms."""
    if n < 0: raise ValueError, 'Input must be a non-negative integer'
    return list(izip(xrange(offset, n+offset), a064389_gen()))

def a064389(n):
    """Returns the term with index n >= 1; offset 1."""
    if n < offset: raise ValueError, 'Input must be an integer >= offset = ' + str(offset)
    return list(islice(a064389_gen(), n-offset, n-offset+1)).pop()